In Cloud Data Centers (CDC), dynamic consolidation of Virtual Machines (VMs) is an efficient technique to increase resource usage and energy efficiency. Energy efficiency has become a new frontier in the virtualized cloud computing paradigm. Data centers must decide how, which, and when VMs must be merged onto a few physical servers, which is a difficult task. Server consolidation necessitates VMs migration, which has a direct influence on service response time. It means that overloading of server results in resource scarcity and application performance deterioration. Most of the existing solutions for VMs consolidation are based on the heuristic methods. The drawbacks of these methods are they produce sub-optimal outcomes and prevent the precise description of a Quality of Service (QoS) target. Further, the requirement for energy efficiency has grown as the number and scale of CDC has grown. Virtual machine migration is widely utilized cloud computing technology that is thus focused in this work to conserve energy. We conduct an in-depth study of the existing literature on that address server consolidation and energy consumption issues and provide optimal solutions. We conclude the survey by describing key challenges for future research on constructing effective and accurate server consolidation techniques with power modeling.